2013年浙江省高中数学竞赛预赛第18题为如下的一道解析几何题:已知抛物线y~2=4x,过x轴上一点K的直线与抛物线交于P、Q两点,证明:存在唯一一点K,使1/PK~2+1/QK~2为常数,并确定点K的坐标.我们自然地想到对于圆锥曲线,是否都能找到某个定点K使得过点K的直线与圆锥曲线交于P、Q两点满足1/PK~2+1/QK~2为常数.下面 In 2013 Zhejiang province high school mathematics contest preliminaries eighteenth is the following analytic geometry problem: The known parabola y ~ 2 = 4x, a straight line passing a point K on the x-axis and parabola at P, Q two points prove that there is a unique A point K, making 1 / PK ~ 2 + 1 / QK ~ 2 a constant and determining the coordinates of point K. We naturally think of whether we can find a fixed point K for a conic, so that the straight line and conic At P, Q two points to meet 1 / PK ~ 2 +1 / QK ~ 2 is constant